Limited data of stochastic load processes and system random variables result in uncertainty in the results of time-dependent reliability analysis. An uncertainty quantification (UQ) framework is developed in this paper for time-dependent reliability analysis in the presence of data uncertainty. The Bayesian approach is employed to model the epistemic uncertainty sources in random variables and stochastic processes. A straightforward formulation of UQ in time-dependent reliability analysis results in a double-loop implementation procedure, which is computationally expensive. This paper proposes an efficient method for the UQ of time-dependent reliability analysis by integrating the fast integration method and surrogate model method with time-dependent reliability analysis. A surrogate model is built first for the time-instantaneous conditional reliability index as a function of variables with imprecise parameters. For different realizations of the epistemic uncertainty, the associated time-instantaneous most probable points (MPPs) are then identified using the fast integration method based on the conditional reliability index surrogate without evaluating the original limit-state function. With the obtained time-instantaneous MPPs, uncertainty in the time-dependent reliability analysis is quantified. The effectiveness of the proposed method is demonstrated using a mathematical example and an engineering application example.
Uncertainty Quantification of Time-Dependent Reliability Analysis in the Presence of Parametric Uncertainty
Manuscript received March 26, 2015; final manuscript received December 4, 2015; published online July 1, 2016. Assoc. Editor: Ioannis Kougioumtzoglou.
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Hu, Z., Mahadevan, S., and Du, X. (July 1, 2016). "Uncertainty Quantification of Time-Dependent Reliability Analysis in the Presence of Parametric Uncertainty." ASME. ASME J. Risk Uncertainty Part B. September 2016; 2(3): 031005. https://doi.org/10.1115/1.4032307
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